The Magpies have been pursuing deals in the transfer market that could have seen Wilson leave the club.
But he is likely to stay for at least this season, even though he will be out on opening weekend with a back injury.
Manager Eddie Howe told reporters: "Callum had an injection in his back. Without going into too much detail on the injury, I think it was a bulge in his disc which needed treatment so he had that operation and I think he may miss the start of the season.
"But thankfully there are not too many games at the start, we’re week to week so hopefully he won’t miss too many."
On new signings, Howe said: "It's very difficult to judge (when to expect progress). I would love to give you definitive answers but if I give you definitive answers you're going to hold me to it and then I'm going to potentially look stupid. We are working to try and bring players in and that won't stop."